Marcus Aurelius (“Aurel”) Stefan
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PROVIDER: S-EPMC1125904 | biostudies-literature | 2003 May
REPOSITORIES: biostudies-literature
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Project description:We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L(1) data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L(∞) data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L(1) data.
| S-EPMC4535267 | biostudies-literature
Project description:Molecular dynamics simulation data for a variety of binary guest mixtures (H2/CO2, Ne/CO2, CH4/CO2, CO2/N2, H2/CH4, H2/Ar, CH4/Ar, Ar/Kr, Ne/Ar, CH4/C2H6, CH4/C3H8, C2H6C3H8, CH4/nC4H10, and CH4/nC5H11) in zeolites (MFI, BEA, ISV, FAU (all-silica), NaY, NaX, LTA, CHA, DDR) and metal-organic frameworks (MOFs) (IRMOF-1, CuBTC, MgMOF-74) show that the Maxwell-Stefan (M-S) diffusivities, Đ 1, Đ 2, Đ 12, are strongly dependent on the molar loadings. The main aim of this article is to develop a fundamental basis for describing the loading dependence of M-S diffusivities. Using the ideal adsorbed solution theory, a thermodynamically rigorous definition of the occupancy, θ, is derived; this serves as a convenient proxy for the spreading pressure, π, and provides the correct metric to describe the loading dependence of diffusivities. Configurational-bias Monte Carlo simulations of the unary adsorption isotherms are used for the calculation of the spreading pressure, π, and occupancy, θ. The M-S diffusivity, Đ i , of either constituent in binary mixtures has the same value as that for unary diffusion, provided the comparison is made at the same θ. Furthermore, compared at the same value of θ, the M-S diffusivity Đ i of any component in a mixture does not depend on it partner species. The Đ i versus θ dependence is amenable to simple interpretation using lattice-models. The degree of correlations, defined by the ratio Đ 1/Đ 12, that characterizes mixture diffusion shows a linear increase with occupancy θ, implying that correlations become increasingly important as pore saturation conditions are approached.
| S-EPMC6275975 | biostudies-literature
Project description:Two forms of the equation for expression of the rate constant for electron transfer through a Marcus-type treatment are discussed. In the first (exergonic) form, the Arrhenius exponential term was replaced by its classical Marcus term; in the second (endergonic) form, the forward rate constant was replaced by the reverse rate constant (the forward rate constant in the exergonic direction), which was expanded to an equivalent Marcus term and multiplied by the equilibrium constant. When the classical Marcus treatment was used, these two forms of the rate equation give identical curves relating the logarithm of the rate constant to the driving force. The Marcus term for the relation between activation free-energy, DeltaG#, reorganization energy, lambda, and driving force, DeltaG(o), derived from parabolas for the reactant and product states, was identical when starting from exergonic or endergonic parabolas. Moser and colleagues introduced a quantum mechanical correction factor to the Marcus term in order to fit experimental data. When the same correction factor was applied in the treatment for the endergonic direction by Page and colleagues, a different curve was obtained from that found with the exergonic form. We show that the difference resulted from an algebraic error in development of the endergonic equation.
| S-EPMC2238675 | biostudies-literature
Project description:This report highlights the importance for neonatologists/pediatricians of considering Marcus Gunn jaw-winking syndrome among differential diagnoses of ptosis. A detailed clinical assessment is crucial to promptly recognize and appropriately manage it.
| S-EPMC7869362 | biostudies-literature
Project description:The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result (Hadži? & Shkoller 2014 Commun. Pure Appl. Math. 68, 689-757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes.
| S-EPMC4535271 | biostudies-literature
Project description:RationaleThis case report describes the Marcus Gunn phenomenon (MGP), an infrequent type of congenital unwanted contractions of facial muscles that occurs in 4%-6% of patients with congenital ptosis. The defining characteristic of MGP is the affected eyelid lifting in a manner similar to the opening of the mouth.Patient concernsIt addresses a 45-year-old man who was examined in the dental clinic with a severely decayed tooth. He exhibited evidence of normal vision and synchronous movement of his lips and eyelid.DiagnosisThe conditions matched those of the autosomal dominant disorder with incomplete penetration, the MGP. The carious tooth was restored without the necessity for any surgical intervention.TreatmentThe patient was given appropriate dental treatment without any surgical intervention for Marcus Gunn Syndrome.OutcomeAfter receiving routine fillings to treat dental caries, the patient stopped complaining of pain.Take-away lessonThis case report reveals insight into a situation that has been speculated to be an example of neural redirection syndrome, in which impulses from the trigeminal nerve's motor unit are naturally redirected into the levator palpebrae superioris muscles of the upper eyelid and the superior pterygoid muscle.
| S-EPMC11340846 | biostudies-literature
Project description:Electron transfer reactions slow down when they become very thermodynamically favorable, a counterintuitive interplay of kinetics and thermodynamics termed the inverted region in Marcus theory. Here we report inverted region behavior for proton-coupled electron transfer (PCET). Photochemical studies of anthracene-phenol-pyridine triads give rate constants for PCET charge recombination that are slower for the more thermodynamically favorable reactions. Photoexcitation forms an anthracene excited state that undergoes PCET to create a charge-separated state. The rate constants for return charge recombination show an inverted dependence on the driving force upon changing pyridine substituents and the solvent. Calculations using vibronically nonadiabatic PCET theory yield rate constants for simultaneous tunneling of the electron and proton that account for the results.
| S-EPMC6681808 | biostudies-literature